Will tsunade die?

She hasn't yet. She is currently in a comatose state. So since she is incapacitated, the council immediately decided to select another hokage, for example when gaara was kidnapped, the sand elders/council wanted to select another kazekage so that other villages wouldn't attack the hidden village of sand knowing the fact that there is no kage protecting it.

So the shortlist for the hokage would either be kakashi and to a lesser extent naruto.